Exercise 31 Page 404

Let's start by recalling the definitions of complementary and supplementary angles.

Complementary Angles	Supplementary Angles
Two angles are complementary if the sum of their measures is $90^{\circ }.$	Two angles are supplementary if the sum of their measures is $180^{\circ }.$

We are told that the measures of two angles are $35^{\circ }$ and $55^{\circ }.$ To determine whether they are complementary, supplementary, or neither, we will calculate the sum of their measures. Since the sum is $90^{\circ },$ the angles are complementary.